Tarshish is a city referred to about a dozen times in the Bible and has been widely accepted as another version of Tartessos. Josephus, the Jewish historian who wrote during the 1st century AD, was confident that it referred to Tarsus in Cilicia, Turkey, the birthplace of St. Paul. The Septuagint Bible uses Karkendonos where it refers to Tarshish in Isaiah 23:1, which was the Greek form of the name for North African Carthage. This could imply that the founders of Carthage and Tarsus were the same. We know that Carthage was founded by Tyrians and we also know that Cilix, a Tyrian, gave his name to Cilicia when he settled it. Andis Kaulins has claimed that Carthage was possibly built on the remains of Tartessos (i)!
Utica was a Phoenician port city on the northern coast of what is now Tunisia. It no longer exists and its site is now some miles inland because of silting. It is also one of a number of suggested locations for Tarshish(f).
Tarshish/Tartessos is thought by many others to be alternative names for Atlantis. There is a consensus that it was a coastal city in Southern Spain, near modern Cadiz. Despite the efforts of many, its location is still unknown, which can probably be explained by the fact that the coastline has altered considerably over time. Adolf Schulten, who was convinced that Tartessos was Atlantis, spent many years searching, unsuccessfully, for Tarshish in Andalusia.
Other locations have been suggested, such as Tharros in Sardinia, Troy and even Malta where Tarxien may be considered an echo of Tarshish. Tharros sometimes referred to as a ‘second Carthage’ had its port located as recently as 2008(d). The suggestion that Tharros was Tarshish was based on their similar-sounding names and the reference to Tarshish in the Phoenician inscription on the ‘Nora Stone’ discovered at Nora on the south coast of Sardinia in 1773.
Quite a variety of locations have been offered as the site of Tarshish(f)(k).
Aaron Arrowsmith (1750-1832), a British cartographer and geographer was of the view that “Tartessus was a territory established by adventurous traders who settled in the Iberian peninsula after moving from the ancient city of Tarsus in Asia Minor (modern Turkey).” 
It is accepted that biblical silver was sourced from ‘Tarshish’, initially assumed to be Tartessos in Spain. Recent studies employing lead isotope tests, when applied to Phoenician silver hoards(g) revealed that both Spain and Sardinia were possible sources. However, it might be argued that the Nora Stone may give Sardinia a somewhat stronger claim.
A more radical idea was put forward in 2012 by the Spanish researcher, José Angel Hernández, who proposed that the Tarshish of the Bible was to be found on the coastal region of the Indus Valley and that Tartessos was a colony of the Indus city of Lhotal and had been situated on both sides of the Strait of Gibraltar!(a)(b) This view is apparently supported by biblical references (1 Kings 9:26, 22:48; 2 Chr. 9:21) that note that the ‘ships of Tarshish’ sailed from Ezion-Geber on the Red Sea’s Gulf of Aqaba!
However, if Tarshish was another name for Atlantis and according to the bible it existed at the time of Solomon, circa 1000 BC, we are confronted with a contradiction of Plato’s 9,000 years elapsing since the destruction of Atlantis and the visit of Solon to Sais. King Jehoshaphat reigned around 860 BC and planned to send a fleet to Tarshish, just 200 years before Solon, so the likelihood of Tarshish being Atlantis is a rather remote possibility.
A recent suggestion by a Dutch commentator, Leon Elshout, places the biblical Tarshish in Britain(h) and is supported by a Christadelphian website(j).